Spatially Resolved Spectroscopy
Nuclear magnetic resonance has been successfully
used in biomedicine for imaging and in vivo spectroscopy. However, both
NMR modes have been severely limited by the availability of excitation
selective only for simple shapes, eg. spherical, cylindrical, or cubic
volumes. We developed new excitation excitation sequence selective for
Completely Arbitrary Regional Volume Excitation (CARVE). CARVE
sequence can be used for high resolution NMR spectroscopy and
volume-selective imaging of precisely delineated organs, tumors, body
To design a desired excitation profile, we chose a sequence of short,
small-flip-angle RF pulses in combination with the constant linear
arbitrarily orientable gradient. The desired excitation profile
resulted from a sequence of N constant intervals, with
small-flip-angle pulses, their phases and the associated gradients. The
gradients were constant within intervals, but were different between
the intervals. Likewise, the tilt angles and the phases of RF pulses
differed between the intervals.
CARVE excitation sequence and corresponding k-space trajectory for the
'A' shaped profile with 100 excitation events.
The application of the completely arbitrary regional volume excitation
(CARVE) in a on resonance spin-system, encompasses three steps. First,
all coefficients for the desired excitation profile in the k-space are
found by nD Fourier transformations (FT) of the excitation profile, and
the N largest complex coefficients are retained together with
the respective k-vectors k. Second, the tip angles and RF
phases are calculated from the Fourier coefficients. The vectors k
are constant and need be visited only once during the excitation
sequence. In contrast to the continuous k-space analysis, the order of
visitation is not important, but different pathways may require
different gradient strengths. The best path to visit N vectors k
is the one with minimum required gradients and minimum gradient
switching. Consequently, in the third step,
the optimal path is found by the use of simulated annealing and by
minimizing the sum of squares of individual gradient pulses.
The process of CARVE sequence calculation: ideal excitation profile,
its transformation into k-space, selection of 100 coefficients with the
highest amplitude and the expected profile after the excitation
During the CARVE sequence magnetization is subjected to rotations by RF
pulses toward or away from the z-axis and rotations by the gradient
steps around the z-axis. Because gradient rotation is spatially
dependent every magnetization component has different trajectory during
the sequence but at the end of the sequence all components within the
profile realign along the y-axis and outside the profile are restored
back along z- axis. This is illustrated in the figure below where
trajectories within and outside the excitation profile are shown. The
arrows in the figure a) show the position of the magnetization
components for which the trajectories are shown in b). Within the
profile, the magnetization components are aligned such that majority of
the RF pulses tip them from the z-axis, (b, left). At the same time the
components outside the profile are randomly tipped toward and away from
the z-axis so that the net effect is no tilt at all, (b right).
Magnetization trajectory during CARVE sequence for a point within the
profile (left) and out of it (right).
Experimental verification. cylindrical tube filled with water (left)
and measured excited 'A' shaped profile in the same tube with the CARVE
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